Chief executive Keith Wyness and secretary Dave Harrison went to the England squad hotel in Manchester for the striker to sign his contract. And Johnson said: "I am looking forward to giving 110% in every game I play in and hopefully I can score goals for Everton."
Moyes is confident of following the deal for Johnson and the loan signing of goalkeeper Tim Howard with the capture of a centre-back.
But there are issues that must be overcome if Everton are to win the race for either of their main targets, Robert Huth of Chelsea and Wolves' Joleon Lescott.
Middlesbrough have joined Everton and Wigan in chasing Huth, who is prepared for showdown talks with Chelsea manager Jose Mourinho.
The Riversiders will match Chelsea's £5.5m asking price for the 21-year-old Germany international.
And the fear is Middlesbrough will offer Huth a salary package that Everton would be struggling to compete against.
Wolves, meanwhile, are still holding out for around £5m for Lescott, with Reading, Aston Villa and Manchester City thought to also be interested.
